Results 1 to 10 of about 6,125 (36)
Smooth affine group schemes over the dual numbers [PDF]
Épijournal de Géométrie Algébrique, 2019 We provide an equivalence between the category of affine, smooth group schemes over the ring of generalized dual numbers $k[I]$, and the category of extensions of the form $1 \to \text{Lie}(G, I) \to E \to G \to 1$ where G is an affine, smooth group ...
Matthieu ROMAGNY, Dajano Tossici
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Periodic balanced binary triangles [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 A binary triangle of size $n$ is a triangle of zeroes and ones, with $n$ rows, built with the same local rule as the standard Pascal triangle modulo $2$.
Jonathan Chappelon
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Transcendental equations satisfied by the individual zeros of Riemann $\zeta$, Dirichlet and modular $L$-functions [PDF]
, 2015 We consider the non-trivial zeros of the Riemann $\zeta$-function and two classes of $L$-functions; Dirichlet $L$-functions and those based on level one modular forms.
França, Guilherme, LeClair, André
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Hyperelliptic curves, continued fractions, and Somos sequences [PDF]
, 2006 We detail the continued fraction expansion of the square root of a monic polynomials of even degree. We note that each step of the expansion corresponds to addition of the divisor at infinity, and interpret the data yielded by the general expansion.
van der Poorten, Alfred J.
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Congruences concerning Jacobi polynomials and Ap\'ery-like formulae [PDF]
, 2012 Let $p>5$ be a prime. We prove congruences modulo $p^{3-d}$ for sums of the general form $\sum_{k=0}^{(p-3)/2}\binom{2k}{k}t^k/(2k+1)^{d+1}$ and $\sum_{k=1}^{(p-1)/2}\binom{2k}{k}t^k/k^d$ with $d=0,1$. We also consider the special case $t=(-1)^{d}/16$ of
Apèry R. +7 more
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Twisted character of a small representation of GL(4)
, 2006 We compute by a purely local method the (elliptic) twisted by transpose-inverse character \chi_{\pi_Y} of the representation \pi_Y=I_{(3,1)}(1_3x\chi_Y) of G=GL(4,F), where F is a p-adic field, p not 2, and Y is an unramified quadratic extension of F ...
Flicker, Yuval Z., Zinoviev, Dmitrii
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Proof of a congruence for harmonic numbers conjectured by Z.-W. Sun
, 2012 For a positive integer $n$ let $H_n=\sum_{k=1}^{n}1/k$ be the $n$th harmonic number. In this note we prove that for any prime $p\ge 7$, $$ \sum_{k=1}^{p-1}\frac{H_k^2}{k^2} \equiv4/5pB_{p-5}\pmod{p^2}, $$ which confirms the conjecture recently ...
Mestrovic, Romeo
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New harmonic number identities with applications [PDF]
, 2009 We determine the explicit formulas for the sum of products of homogeneous multiple harmonic sums $\sum_{k=1}^n \prod_{j=1}^r H_k(\{1\}^{\lambda_j})$ when $\sum_{j=1}^r \lambda_j\leq 5$.
Tauraso, Roberto
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Sharpenings of Li's criterion for the Riemann Hypothesis
, 2006 Exact and asymptotic formulae are displayed for the coefficients $\lambda_n$ used in Li's criterion for the Riemann Hypothesis. For $n \to \infty$ we obtain that if (and only if) the Hypothesis is true, $\lambda_n \sim n(A \log n +B)$ (with $A>0$ and $B$
A. Voros +15 more
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Counting $r$-tuples of positive integers with $k$-wise relatively prime components
, 2016 Let $r\ge k\ge 2$ be fixed positive integers. Let $\varrho_{r,k}$ denote the characteristic function of the set of $r$-tuples of positive integers with $k$-wise relatively prime components, that is any $k$ of them are relatively prime.
Tóth, László
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